Non-paritious Hilbert modular forms

Autor: Ariel Pacetti, David Loeffler, Lassina Dembélé
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET
Mathematische Zeitschrift
ISSN: 0025-5874
Popis: The arithmetic of Hilbert modular forms has been extensively studied under the assumption that the forms concerned are "paritious" -- all the components of the weight are congruent modulo 2. In contrast, non-paritious Hilbert modular forms have been relatively little studied, both from a theoretical and a computational standpoint. In this article, we aim to redress the balance somewhat by studying the arithmetic of non-paritious Hilbert modular eigenforms. On the theoretical side, our starting point is a theorem of Patrikis, which associates projective l-adic Galois representations to these forms. We show that a general conjecture of Buzzard and Gee actually predicts that a strengthening of Patrikis' result should hold, giving Galois representations into certain groups intermediate between GL(2) and PGL(2), and we verify that the predicted Galois representations do indeed exist. On the computational side, we give an algorithm to compute non-paritious Hilbert modular forms using definite quaternion algebras. To our knowledge, this is the first time such a general method has been presented. We end the article with a selection of examples.
Final version, to appear in Math Zeitschrift
Databáze: OpenAIRE
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